Conformal regularization of Einstein's field equations
Abstract
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a conformal orthonormal frame, we obtain a coupled system of differential equations for a set of dimensionless variables, associated with the conformal dimensionless metric, where the variables describe ratios with respect to the chosen asymptotic scale structure. As examples, we describe some explicit choices of conformal factors and coordinates appropriate for the situation of a timelike congruence approaching a singularity. One choice is shown to just slightly modify the socalled Hubblenormalized approach, and one leads to dimensionless firstorder symmetric hyperbolic equations. We also discuss differences and similarities with other conformal approaches in the literature, as regards, e.g., isotropic singularities.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 September 2005
 DOI:
 10.1088/02649381/22/17/026
 arXiv:
 arXiv:grqc/0504063
 Bibcode:
 2005CQGra..22.3775R
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 New title plus corrections and text added. To appear in CQG